Write your solutions clearly and legibly. no credit will be given for


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INSTRUCTIONS

• Read each inquiry carefully, and reply each inquiry altogether.

• Show all of your effect. No faith accomplish be attached for unsupported replys.

• Write your solutions palpably and legibly. No faith accomplish be attached for

illegible solutions.

1. (10 points) Evaluate

1

0

e

x

x

dx or recite that it diverges.

# PTS

1

2

3

4

5

6

B

S

Σ

2. (10 points) Evaluate

xe

−2x

sin(2x) dx. You may permission your reply as

unsimplified multifarious exponentials—that is, your ultimate reply may contain

imaginary bulk.

2

3. (10 points) Simplify and express

(

1

2

+

1

2

ı

)

2+2ı

as a multifarious reckon a + bı, where a and b are developed bulk.

4. (10 points) Find M6

for

3

−3

ln(x

2

+ 1) dx.

3

5. (10 points) Evaluate

x

3

+ 1

x(x

2

− 1)

dx

4

6. (10 points) Find the area of the vital loop of the limaçon r = 2 cos θ − 1

pictured beneath.

0.5 1.0 1.5 2.0 2.5 3.0

- 1.5

- 1.0

- 0.5

0.5

1.0

1.5

5

BONUS QUESTION (5 EXTRA CREDIT POINTS):

Show that if f (x) = rx + s is a direct duty (r, s constants) then

T

N =

b

a

f (x) dx

for all N and all endpoints a, b.

SURVEY QUESTION (5 EXTRA CREDIT POINTS):

To be attached.

6

 

 

for unmeasured inquiry see attachment